Single- and multi-modality alignment of medical images in the presence of non-rigid deformations using phase correlation

ABSTRACT

A phase correlation method (PCM) can be used for translational and/or rotational alignment of 3D medical images even in the presence of non-rigid deformations between first and second images of a registered volume of a patient.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 120 to U.S.application Ser. No. 16/036,701 filed 16 Jul. 2018 and Ser. No.14/559,880 filed 3 Dec. 2014, which claims priority under 35 U.S.C. §119(e) to U.S. Provisional Application No. 61/911,379 filed 3 Dec. 2013,the disclosures of each are incorporated by reference herein.

TECHNICAL FIELD

The subject matter described herein relates to use of phase correlationas a tool for single- and multi-modality translational alignment ofmedical images in the presence of non-rigid deformations.

BACKGROUND

Translational image alignment is a fundamental and commonly usedpreprocessing step in many medical imaging operations, such as imageregistration, image fusion, multiframe imaging, etc. In manyapplications, it can be crucial that the alignment algorithm is fast androbust to noise. The problem of image alignment becomes even morechallenging when there are small deformations present in the images (forexample, deformations due to patient breathing and organ movement) orwhen different types of imaging modalities produce the two images beingregistered. In such cases, intensity-based similarity measures canexhibit non-convex behavior, which renders the problem difficult foroptimization. An example of such difficulties is illustrated in of FIG.1, which shows a graph 100 depicting values of a cross correlationsimilarity measure as a function of the translational shift along thepatient axis for a pair of images of the pelvis area of a patient'sbody. The graph 100 of FIG. 1 shows, among other things, how thepresence of local maxima can cause difficulties in solving for theglobal maximum with gradient based optimization approaches.

SUMMARY

Consistent with implementations of the current subject matter, a phasecorrelation method (PCM) can be used reliably for translational and/orrotational alignment of 3D medical images in the presence of non-rigiddeformations in the datasets.

In one aspect, a method includes comparing a first medical image of afirst registered volume of a patient taken at a first time and a secondmedical image of a second registered volume of the patient taken at asecond time using a phase correlation method. The comparing includescalculating at least one of a translation and a rotation required toproperly align the first and second medical images in a commonregistration grid. The method further includes determining a change toat least one of a physical location and a physical orientation of thepatient based on the calculating. The change corrects a second positionof the patient as imaged in the second image to more closely conform toa first position of the patient imaged in the first image. The change isoutputted.

In optional variations, one of more of the following features can beincluded in any feasible combination. The first image and the secondimage can be obtained using a same imaging modality or differing imagingmodalities. The first registered volume and the second registered volumecan be downsampled to create the common registration grid having a lowerresolution than either of the first registered volume and the secondregistered volume. Alternatively or in addition, a determination can bemade that the first registration volume and the second registrationvolume include different resolutions, and the first registration volumeand/or the second registration volume can be resampled on the commonregistration grid. A common resolution along each dimension of thecommon registration grid can be set to a coarser of a first initialresolution of the first registered volume and a second initialresolution of the second registered volume.

The comparing can include identifying a peak in a normalized cross-powerspectrum of the first registered volume and the second registeredvolume. The identifying of the peak in the normalized cross-powerspectrum can include finding a maximum intensity of a Fourier transformof the normalized cross-power spectrum and selecting, from a pluralityof voxels having intensities greater than a threshold, a voxel for whicha sum of voxel intensities of neighboring voxels around the voxel ishighest. The neighboring voxels can be in a window defined as a fractionof a number of voxels along each dimension of the common registrationgrid. The method can further include refining a position of the peak bycalculating a centroid of the voxel intensities of the neighboringvoxels.

In some variations, the change can be applied to the physical locationand/or the physical orientation of the patient, and a medical procedurecan be performed on the patient after applying the change. The medicalprocedure can include at least one of a radiation treatment and asurgical procedure.

Systems and methods consistent with this approach are described as wellas articles that comprise a tangibly embodied machine-readable mediumoperable to cause one or more machines (e.g., computers, etc.) to resultin operations described herein. Similarly, computer systems are alsodescribed that may include a processor and a memory coupled to theprocessor. The memory may include one or more programs that cause theprocessor to perform one or more of the operations described herein.

A system consistent with implementations of the current subject mattercan optionally include one or more imaging devices (e.g. MR, CT, or thelike) for generating the first and second medical images. A system neednot include such devices. For example, the first and second medicalimages can be generated by other imaging devices and the images (or atleast one or more datasets representing the images) can be transferredto computer hardware executing the operations described herein.

The details of one or more variations of the subject matter describedherein are set forth in the accompanying drawings and the descriptionbelow. Other features and advantages of the subject matter describedherein will be apparent from the description and drawings, and from theclaims.

DESCRIPTION OF DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, show certain aspects of the subject matterdisclosed herein and, together with the description, help explain someof the principles associated with the disclosed implementations. In thedrawings,

FIG. 1 shows a graph depicting values of a cross correlation similaritymeasure as a function of the translational shift along the patient axisfor a pair of images of the pelvis area of a patient's body;

FIG. 2 shows a table of parameters for example registration datasets;

FIG. 3 shows a series of images illustrating translational alignment ofa single-modality MR dataset using a PCM approach consistent withimplementations of the current subject matter depicting initial positionof the volumes (e.g. misaligned along the patient axis) before the PCMregistration;

FIG. 4 shows a series of images illustrating translational alignment ofa single-modality MR dataset using the PCM approach consistent withimplementations of the current subject matter depicting the registeredvolumes after applying the PCM shift;

FIG. 5 shows a series of images illustrating translational alignment ofa multi-modality MR/CT dataset consistent with implementations of thecurrent subject matter;

FIG. 6 and FIG. 7 show graphs depicting behavior of the CC and MIregistration cost functions around a PCM shift obtained consistent withimplementations of the current subject matter;

FIG. 8 shows a table listing registration results for the datasetslisted in the table of FIG. 2;

FIG. 9 shows a table containing results obtained with downsampledvolumes using a downsampling factor of 2 for each dimension consistentwith implementations of the current subject matter; and

FIG. 10 shows a process flow diagram illustrating aspects of a methodhaving one or more features consistent with implementations of thecurrent subject matter.

When practical, similar reference numbers denote similar structures,features, or elements.

DETAILED DESCRIPTION

Approaches consistent with the current subject matter can be used forsingle-modality as well as for multi-modality image registration, forexample for registration of two images captured using a same ordiffering modalities, where possible modalities include but are notlimited to magnetic resonance (MR), computed tomography (CT), and thelike. Registration quality can be quantified using cross correlation(CC) and mutual intensity (MI) intensity-based similarity measures (SM)as registration cost functions. The cost function values obtained with aPCM consistent with implementations of the current subject matter arecomparable to optimum values found with an exhaustive search and yieldgood agreement. The obtained PCM shifts can closely match optimum shiftsfound using an exhaustive search, both for single-modality (e.g. MR toMR, CT to CT, etc.) registrations and multi-modality (e.g. MR to CT, orthe like) registrations. Accordingly, a PCM consistent withimplementations of the current subject matter can be an efficient androbust method for coarse image alignment with pixel-level accuracy. Thesimplicity of the algorithm, together with its small computationalcomplexity, can make it an advantageous choice as a tool for fastinitial alignment in medical image processing.

The phase correlation method (PCM) is an efficient and robust to noisealgorithm for image alignment, which was originally used to estimatetranslational integer-pixel shifts between displaced images. Later, thealgorithm was extended to also work with rotated and scaled 2D images byusing a log-polar transform of the images. Similar generalizations ofthe PCM for combined translation, rotation and scaling estimation in the3D case are not possible, since there is no coordinate transformationthat converts rotation to translation in the 3D case. However, themethod was extended to register 3D translated and rotated volumes byutilizing the pseudopolar Fourier transform and, alternatively, byapplying an iterative optimization procedure called cylindrical phasecorrelation method (CPCM). In the latter approach, the rotation anglearound different axes is iteratively estimated by applying the PCM tocylindrically mapped images.

Consistent with implementations of the current subject matter,application of the PCM in its original form is used for reliably andrelatively computationally inexpensively aligning pairs of 3D volumesthat are not only translated, but also deformed with respect to eachother. The algorithm produces very good results when applied tomulti-modality MR/CT image registration and can provide near-optimumresults in terms of two commonly used intensity-based similaritymeasures. The differences between the optimum shift (e.g. one found byan exhaustive search) and a shift identified by a PCM consistent withimplementations of the current subject matter are small. Use of thecurrent subject matter can further broaden the application of the PCM inclinical practice of alignment of two or more medical images.

The Phase Correlation Method (PCM) is based on the fundamental Fouriershift theorem. The theorem states that delaying (shifting) the signalf(t) with an interval τ is equivalent to multiplying the signal'sFourier transform, F(ω), by e^(−iωτ), for example as expressed inequation 1:

f(t−τ)=e ^(−iωτ) F(ω)  (1)

Therefore, if two volumes A and B are shifted versions of each other(i.e. B=({right arrow over (x)}−{right arrow over (Δ)})=A({right arrowover (x)}), their normalized cross-power spectrum, Q({right arrow over(k)}), simplifies to an expression such as that in equation 2:

$\begin{matrix}{{Q( \overset{arrow}{k} )} = {\frac{{F_{A}( \overset{arrow}{k} )}{F_{B}^{*}( \overset{arrow}{k} )}}{{{F_{A}( \overset{arrow}{k} )}{F_{B}^{*}( \overset{arrow}{k} )}}} = {\frac{{F_{A}( \overset{arrow}{k} )}{F_{A}^{*}( \overset{arrow}{k} )}e^{i{\overset{arrow}{k} \cdot \overset{arrow}{\Delta}}}}{{{F_{A}( \overset{arrow}{k} )}{F_{A}^{*}( \overset{arrow}{k} )}e^{i{\overset{arrow}{k} \cdot \overset{arrow}{\Delta}}}}} = e^{i{\overset{arrow}{k} \cdot \overset{arrow}{\Delta}}}}}} & (2)\end{matrix}$

-   -   where F_(A) ({right arrow over (k)}) and F_(B)({right arrow over        (k)}) are the Fourier transforms of the images A and B, and        F_(B)*({right arrow over (k)}) is the complex conjugate of        F_(B)({right arrow over (k)}). Calculating the inverse Fourier        transform q({right arrow over (x)}) of the normalized        cross-power spectrum gives a Kronecker delta function, centered        exactly at the displacement, {right arrow over (Δ)}, which is        the peak of the normalized cross-power spectrum. The Kronecker        delta function can be expressed as in equation 3:

q({right arrow over (x)})=δ({right arrow over (Δ)})  (3)

In the ideal case of a second image B being a translated replica of afirst image A, the position of the peak identifies the exacttranslational misalignment between the images. However, due to noiseand/or deformations normally being present in real images, the peak isusually spread around neighboring voxels. Also, aliasing artifacts andedge effects can additionally degrade the quality of the peak.Previously available approaches for improving the clarity and sharpnessof the PCM peak and for reaching sub-pixel accuracy generally cannot beapplied directly for the case of deformed volumes and multi-modalityimage registration, since the basic assumption of the approaches, thatthe two images being registered are identical (to the extent of somerandom noise being present in both images), is not valid. Therefore, forregistration applications in medical imaging, pixel-level alignmentaccuracy may be considered. In one implementation consistent with thecurrent subject matter, the position of the peak can be identified witha simple thresholding technique as discussed in more detail below.

The table of parameters 200 reproduced in FIG. 2 shows variousinformation about registration datasets used in experimental validationof aspects of the current subject matter. The first column contains theidentification name of the dataset, the second column contains the typeof registration for the corresponding data set, the “Volume1” and“Volume2” columns contain information about the two 3D volumes beingregistered (imaging modality, number of voxels and voxel size), and thelast column gives information about which part of the anatomy of thepatient was scanned. All datasets are obtained from real scans of humanpatients. Each dataset contains a pair of two misaligned 3D volumes,obtained in two different scans of the same patient. The differentdatasets cover different portions of the patient's body and can exhibitlarge translational displacements in all three directions. Scans of thethorax and the abdomen portions are also subjected to deformations dueto patient breathing and movement. In some of the datasets, the imagingmodalities used for the two scans differ.

The performance of the PCM used in a manner consistent withimplementations of the current subject matter to align misaligned imageswas investigated in three scenarios, which are discussed in more detailbelow. In the first scenario, the PCM is used to align deformed volumesobtained with the same imaging modality (datasets “DS1”, “DS2”, “DS3”and “DS4” in the table 200 of FIG. 2). All of these datasets wereproduced via MR scans. In the second scenario, the PCM is used toregister multi-modality MR/CT pairs (datasets “DS5”, “DS6”, “DS7” and“DS8” in the table 200 of FIG. 2). In the MR scans, the couch and thehead support on which the patient is laying are not visible. In order toeliminate any effects due to the presence of these objects in the CTdata, they were cropped out manually from the CT scans. The effect onthe registration results attributable to the couch and the head supportbeing present in the CT scans is investigated in the third scenario(datasets “DS5C”, “DS6C”, “DS7C” and “DS8C” in the table 200 of FIG. 2).The datasets are practically identical to the datasets used in thesecond scenario, except that in this case the couch and the head supportare not cropped out from the CT scans.

Due to the deformations present in the registration datasets, it isdifficult to define the optimal alignment shifts for the datasets usedin this work. Therefore, to evaluate the accuracy of the PCMregistration, two similarity measures are used as registration costfunctions: the cross correlation coefficient (CC) and the mutualinformation (MI) between the two volumes A and B, for example asexpressed in equations 4 and 5:

$\begin{matrix}{{CC} = \frac{\sum\limits_{i}\; {( {A_{i} - \overset{¯}{A}} )( {B_{i} - \overset{¯}{B}} )}}{\sqrt{\sum\limits_{i}\; {( {A_{i} - \overset{¯}{A}} )^{2}{\sum( {B_{i} - \overset{¯}{B}} )^{2}}}}}} & (4) \\{{MI} = {\sum\limits_{i}{\sum\limits_{j}{{P( {A_{i},B_{J}} )}\log \frac{P( {A_{i},B_{J}} )}{{p( A_{i} )}{p( B_{J} )}}}}}} & (5)\end{matrix}$

Here, A_(i) and B_(i) are the image intensities of the i-th voxel in thevolumes A and B, P(A_(i),B_(j)) is the joint probability densityfunction of the voxel intensities in the two volumes, and p(A_(i)) andp(B_(j)) are the marginal probability density functions of A and Brespectively. A histogram with 16×16 bins was used to evaluateP(A_(i),B_(j)).

The obtained similarity measures after applying the shift from the PCMare compared to the optimum (maximum) values of the measures found withan exhaustive search on a large grid of shifts around the PCM shift. TheCC and MI registration metrics were selected for the purposes of thiswork. The CC metric is generally suitable for single-modality imageregistration, while the MI metric is more appropriate for multi-modalityregistration.

In an implementation, a PCM algorithm consistent with implementations ofthe current subject matter can be implemented in software (e.g. C++ orthe like). The fast Fourier transformations (FFTs) can be performedusing the FFTW3 library. If the first and second registered volumes inthe first and second images have different resolutions (e.g. differentnumbers of voxels and/or different voxel sizes), the registered volumescan be resampled on a common registration grid. The resolution alongeach dimension of the common registration grid is set to the coarserresolution for that dimension among the two initial resolutions (e.g. afirst initial resolution of the first registered volume or a secondinitial resolution of the second registered volume). The resampling canbe performed using trilinear interpolation. The resampling and the 3DFFTs can be multi-threaded to speed up the execution. Othercomputational approaches are within the scope of the current subjectmatter.

Some implementations can involve an optional preprocessing step in whichthe skin surface of the patient is identified in each of the tworegistered volumes in the registration dataset, before applying the PCM.All voxels that are outside of the surface can be zeroed to reduce theinfluence of noise and other artifacts on the registration results. Theskin surface can be automatically detected by applying a marchingsquares algorithm to all transverse slices of the volumes. Theisosurface for the marching squares algorithm can be set to 0.5 timesthe average intensity of the voxels in volume.

The identification of the peak in the matrix q({right arrow over (x)})(see equation 3) can be performed by first finding the maximumintensity, q_(max). Then, among all voxels with intensity greater than athreshold (e.g. 0.9×q_(max)), the voxel for which the sum of voxelintensities in a small window around that voxel (e.g. neighboringvoxels) is highest can be selected. The size of the window is(wN_(x))×(wN_(y))×(wN_(z)) where w=0.05 (or some other fraction) andN_(x), N_(y), and N_(z) are the number of voxels along each dimension ofthe registration grid. The position of the peak (i.e. the translationalshifts) can be further refined by calculating the centroid of the voxelintensities in the matrix q({right arrow over (x)}) inside the window.

Performance of PCM registration for the illustrative examples can befirst evaluated by visually inspecting the registered volumes. Toperform the inspection, the two volumes are overlaid on a common grid.The first volume is plotted in a first color (e.g. red) and the secondvolume is plotted in a second color (e.g. green). In this way,overlapping areas reflect a blend of the colors, while areas of mismatchare visible in either of the first and second colors. Some examples ofthe PCM registration are depicted in FIG. 3, FIG. 4, and FIG. 5.

FIG. 3 shows a series of images 300 illustrating translational alignmentof a single-modality MR dataset using a PCM approach consistent withimplementations of the current subject matter, where 9 transverse slicesof the two 3D volumes in the dataset (slice numbers are shown at thebottom of each slice) are shown overlaid. The series 300 shows theinitial positions of the two volumes (e.g. misaligned along the patientaxis) before PCM registration consistent with implementations of thecurrent subject matter is applied. FIG. 4 shows a second image series400 in which the registered volumes are better aligned after applyingthe PCM shift consistent with implementations of the current subjectmatter. As shown in FIG. 3 and FIG. 4, the two volumes are aligned verywell after registration, except for the areas of small deformations,which cannot be registered with simple rigid translations.

FIG. 5 shows a series of images 500 illustrating an example of amulti-modality MR to CT registration. The series 500 shows sagital,coronal and transverse slices, before and after the PCM registration.This example illustrates the good performance of a PCM approachconsistent with implementations of the current subject matter for casesin which the two volumes are strongly misaligned. Note that even thoughthe CT couch and head support are not cropped out from the CT scan, thePCM approach consistent with implementations of the current subjectmatter nonetheless provides very good registration results. Similarresults were obtained for all other tested datasets. From the visualinspection, it is evident that the PCM registration finds anearly-optimum translational shift for registering the volumes.

To compare the obtained shifts with the best shifts possible (in termsof the registration cost functions), an exhaustive search over the shiftparameters can be performed. FIG. 6 and FIG. 7 show charts 600, 700illustrating the typical behavior of the CC and MI registration costfunction for different transverse shifts, relative to the shift found bya PCM approach consistent with implementations of the current subjectmatter (hereafter, referred to as “the PCM shift”). The axes in thecharts 600, 700 correspond to the additional shift being applied to theregistered volumes after the initial translation found by the PCMapproach of the current subject matter. To produce the charts 600, 700of FIG. 6 and FIG. 7, the two cost functions were calculated fortransverse shifts on a 10×10 voxel grid with a step of 0.5 voxels. Thecoordinates of the points in the charts 600, 700 correspond to theadditional shifts being added to the initial PCM shift.

The registration results for all tested datasets are summarized in thetable 800 of FIG. 8, which shows the CC and MI values for the shiftfound by the PCM. The table 800 also contains information about theoptimum values of the CC and MI similarity measures, which were found bythe exhaustive search approach around the initial PCM shift. The firstcolumn contains the identification name of the dataset, the secondcolumn contains information about the size of the registration grid onwhich the original volumes are resampled, the third and fourth columnsshow the values of the similarity measures after applying the obtainedPCM shift, the next columns show the additional shifts (that need to beadded to the PCM shift) and the corresponding optimum values of thesimilarity measures obtained with exhaustive search around the PCMshift, and the last column contains the execution times of the developedalgorithm.

The optimum shifts shown in the table are the additional shifts thatneed to be added to the PCM shift, in order to obtain the optimum valuesof the similarity measures. It can be seen that the shifts obtained withthe PCM registration approach consistent with implementations of thecurrent subject matter are very close to the optimum shifts. In manycases, the PCM shift in the transverse plane is within 1 voxel (1.5 mm)from the optimum shift. Considering the CC metric in the single-modalitycases and the MI metric in the multi-modality cases, for nine out of thetwelve example datasets there is a perfect alignment along the patientaxis. The obtained cost function values are generally within 1.5% fromthe optimum values. The largest deviations from the optimum shifts areobserved for the thorax-abdomen datasets (“DS5”, “DS5C”, “DS7” and“DS7C”). Visual inspection of these particular cases reveals that, dueto large deformations in this area of the patient's body, simpletranslations may not be enough to obtain good alignment of the entirevolumes in some cases. Both a PCM shift approach consistent withimplementations of the current subject matter and the optimum shifts mayprovide only partial alignments of different sections of the anatomy inthese cases.

The total execution time of the algorithm for each dataset is shown inthe last column in the table 800 of FIG. 8. The performance of thealgorithm in terms of execution speed can be further improved bydownsampling the initial 3D volumes to a lower resolution grid andapplying the PCM approach consistent with implementations of the currentsubject matter to the downsampled volumes.

The table 900 of FIG. 9 contains the registration results obtained withdownsampled volumes. The ΔCC and ΔMI columns show the relativedifference between the corresponding registration cost functionsobtained with and without the downsampling step-positive valuesindicating improved performance when the downsampling is used, and thelast two columns show the execution times when the downsampling isperformed and the corresponding speedup factor, compared to the timingresults without downsampling. The downsampling factor for each dimensionis 2 in this example. Downsampling the volumes can improve the executionspeed by a factor of approximately 3 to 8 in at least some cases,depending on the size of the registration grid. The downsampling doesnot significantly degrade the quality of the registration and in somecases better results are observed. This effect can be explained by thelower noise level in the resampled volume, due to the averaging ofnearby voxel intensities.

FIG. 10 shows a process flow chart 1000 illustrating features that canbe included in a method consistent with an implementation of the currentsubject matter. At 1002 a first medical image of a first registeredvolume of a patient taken at a first time and a second medical image ofa second registered volume of the patient taken at a second time arecompared using a phase correlation method to calculate at least one of atranslation and a rotation required to properly align the first andsecond medical images. At 1004, a change to at least one of a physicallocation and a physical orientation of the patient is determined forcorrecting a second position of the patient to more closely conform to afirst position of the patient in the first image. The change isdetermined based on the calculated translation and/or the rotationrequired to properly align the first medical image and the secondmedical image. The change can be outputted, for example by displayingone or more parameters to a technician or other user. The displaying canoccur via a printout, a display device, or the like. In other examples,the outputting of the change can include commands to automaticallytranslate and/or rotate a patient, for example by causing movement of apatient couch or bed upon which the patient rests. At 1006, a medicalprocedure can optionally be performed on the patient after applying thedetermined change to the physical location and/or the physicalorientation of the patient. The medical procedure can include radiationtreatment, a surgical procedure, or the like.

As an example, a patient undergoing radiation treatment can be imagedbefore, during, after, etc. delivery of a first radiation fraction. Theresulting image can be considered the first medical image. Prior to asecond radiation fraction delivery to the patient, the patient can beimaged to produce the second medical image. Approaches discussed hereincan be used to determined translational and/or rotational movements ofthe patient necessary to place the patient in a same location andorientation for the second radiation fraction delivery as for the firstradiation fraction delivery.

One or more aspects or features of the subject matter described hereincan be realized in digital electronic circuitry, integrated circuitry,specially designed application specific integrated circuits (ASICs),field programmable gate arrays (FPGAs) computer hardware, firmware,software, and/or combinations thereof. These various aspects or featurescan include implementation in one or more computer programs that areexecutable and/or interpretable on a programmable system including atleast one programmable processor, which can be special or generalpurpose, coupled to receive data and instructions from, and to transmitdata and instructions to, a storage system, at least one input device,and at least one output device.

These computer programs, which can also be referred to programs,software, software applications, applications, components, or code,include machine instructions for a programmable processor, and can beimplemented in a high-level procedural language, an object-orientedprogramming language, a functional programming language, a logicalprogramming language, and/or in assembly/machine language. As usedherein, the term “machine-readable medium” refers to any computerprogram product, apparatus and/or device, such as for example magneticdiscs, optical disks, memory, and Programmable Logic Devices (PLDs),used to provide machine instructions and/or data to a programmableprocessor, including a machine-readable medium that receives machineinstructions as a machine-readable signal. The term “machine-readablesignal” refers to any signal used to provide machine instructions and/ordata to a programmable processor. The machine-readable medium can storesuch machine instructions non-transitorily, such as for example as woulda non-transient solid-state memory or a magnetic hard drive or anyequivalent storage medium. The machine-readable medium can alternativelyor additionally store such machine instructions in a transient manner,such as for example as would a processor cache or other random accessmemory associated with one or more physical processor cores.

To provide for interaction with a user, one or more aspects or featuresof the subject matter described herein can be implemented on a computerhaving a display device, such as for example a cathode ray tube (CRT) ora liquid crystal display (LCD) or a light emitting diode (LED) monitorfor displaying information to the user and a keyboard and a pointingdevice, such as for example a mouse or a trackball, by which the usermay provide input to the computer. Other kinds of devices can be used toprovide for interaction with a user as well. For example, feedbackprovided to the user can be any form of sensory feedback, such as forexample visual feedback, auditory feedback, or tactile feedback; andinput from the user may be received in any form, including, but notlimited to, acoustic, speech, or tactile input. Other possible inputdevices include, but are not limited to, touch screens or othertouch-sensitive devices such as single or multi-point resistive orcapacitive trackpads, voice recognition hardware and software, opticalscanners, optical pointers, digital image capture devices and associatedinterpretation software, and the like. A computer remote from ananalytical system (e.g. an imaging system) can be linked to theanalytical system over a wired or wireless network to enable dataexchange between the analytical system and the remote computer (e.g.receiving data at the remote computer from the analyzer and transmittinginformation such as calibration data, operating parameters, softwareupgrades or updates, and the like) as well as remote control,diagnostics, etc. of the analytical system.

In the descriptions above and in the claims, phrases such as “at leastone of” or “one or more of” may occur followed by a conjunctive list ofelements or features. The term “and/or” may also occur in a list of twoor more elements or features. Unless otherwise implicitly or explicitlycontradicted by the context in which it is used, such a phrase isintended to mean any of the listed elements or features individually orany of the recited elements or features in combination with any of theother recited elements or features. For example, the phrases “at leastone of A and B;” “one or more of A and B;” and “A and/or B” are eachintended to mean “A alone, B alone, or A and B together.” A similarinterpretation is also intended for lists including three or more items.For example, the phrases “at least one of A, B, and C;” “one or more ofA, B, and C;” and “A, B, and/or C” are each intended to mean “A alone, Balone, C alone, A and B together, A and C together, B and C together, orA and B and C together.” Use of the term “based on,” above and in theclaims is intended to mean, “based at least in part on,” such that anunrecited feature or element is also permissible.

The subject matter described herein can be embodied in systems,apparatus, methods, and/or articles depending on the desiredconfiguration. The implementations set forth in the foregoingdescription do not represent all implementations consistent with thesubject matter described herein. Instead, they are merely some examplesconsistent with aspects related to the described subject matter.Although a few variations have been described in detail above, othermodifications or additions are possible. In particular, further featuresand/or variations can be provided in addition to those set forth herein.For example, the implementations described above can be directed tovarious combinations and subcombinations of the disclosed featuresand/or combinations and subcombinations of several further featuresdisclosed above. In addition, the logic flows depicted in theaccompanying figures and/or described herein do not necessarily requirethe particular order shown, or sequential order, to achieve desirableresults. Other implementations may be within the scope of the followingclaims.

What is claimed is:
 1. A system comprising: at least one programmableprocessor; and a non-transitory machine-readable medium storinginstructions which, when executed by the at least one programmableprocessor, cause the at least one programmable processor to performoperations comprising: receiving a first medical image of a patienttaken at a first time and at a first position and a second medical imageof the patient taken at a second time and at a second position, thefirst medical image and the second medical image being different fromeach other due to a deformation; identifying a skin surface of thepatient in the first medical image or the second medical image; zeroingat least one voxel in the first medical image or the second medicalimage that is outside the skin surface; comparing, after the zeroing,the first medical image and the second medical image using a phasecorrelation method to determine a displacement; determining, based onthe displacement, a change to a physical location of the patient; andcorrecting, based on the determined change, the second position of thepatient to more closely conform to a first position of the patient. 2.The system of claim 1, wherein the skin surface is identified in thefirst medical image and the second medical image.
 3. The system of claim2, the identifying further comprising applying a marching squaresalgorithm to a plurality of slices of the first medical image and thesecond medical image.
 4. The system of claim 3, wherein the slices aretransverse slices.
 5. The system of claim 3, wherein an isosurface forthe marching squares algorithm is 0.5 times an average intensity of thevoxels in the first medical image and the second medical image.
 6. Thesystem of claim 1, the comparing comprising: calculating an inverseFourier transform of a cross-power spectrum of the first medical imageand the second medical image, the inverse Fourier transform having apeak spread around neighboring voxels due to the deformation; andcalculating the displacement based at least partially on the intensitiesof the neighboring voxels.
 7. The system of claim 6, the calculating ofthe displacement further comprising: finding a maximum intensity of theinverse Fourier transform of the cross-power spectrum; and selecting asthe peak, from a plurality of voxels having intensities greater than athreshold determined based on the maximum intensity, a voxel for which asum of voxel intensities of the neighboring voxels around the voxel ishighest, wherein the neighboring voxels are in a window sized as afraction of a number of voxels along each dimension of a commonregistration grid.
 8. The system of claim 7, further comprisingdetermining the displacement of the peak by calculating a centroid ofthe voxel intensities of the neighboring voxels inside the window. 9.The system of claim 1, wherein the first medical image and the secondmedical image are obtained using different imaging modalities.
 10. Thesystem of claim 1, the correcting comprising causing translating apatient by causing movement of a patient couch or bed.
 11. Amachine-readable medium storing instructions that, when executed by atleast one programmable processor, cause the at least one programmableprocessor to perform operations comprising: receiving a first medicalimage of a patient taken at a first time and at a first position and asecond medical image of the patient taken at a second time and at asecond position, the first medical image and the second medical imagebeing different from each other due to a deformation; identifying a skinsurface of the patient in the first medical image or the second medicalimage; zeroing at least one voxel in the first medical image or thesecond medical image that is outside the skin surface; comparing, afterthe zeroing, the first medical image and the second medical image usinga phase correlation method to determine a displacement; determining,based on the displacement, a change to a physical location of thepatient; and correcting, based on the determined change, the secondposition of the patient to more closely conform to a first position ofthe patient.
 12. The machine-readable medium of claim 11, wherein theskin surface is identified in the first medical image and the secondmedical image.
 13. The machine-readable medium of claim 12, theidentifying further comprising applying a marching squares algorithm toa plurality of slices of the first medical image and the second medicalimage.
 14. The machine-readable medium of claim 13, wherein the slicesare transverse slices.
 15. The machine-readable medium of claim 13,wherein an isosurface for the marching squares algorithm is 0.5 times anaverage intensity of the voxels in the first medical image and thesecond medical image.
 16. The machine-readable medium of claim 11, thecomparing comprising: calculating an inverse Fourier transform of across-power spectrum of the first medical image and the second medicalimage, the inverse Fourier transform having a peak spread aroundneighboring voxels due to the deformation; and calculating thedisplacement based at least partially on the intensities of theneighboring voxels.
 17. The machine-readable medium of claim 16, thecalculating of the displacement further comprising: finding a maximumintensity of the inverse Fourier transform of the cross-power spectrum;and selecting as the peak, from a plurality of voxels having intensitiesgreater than a threshold determined based on the maximum intensity, avoxel for which a sum of voxel intensities of the neighboring voxelsaround the voxel is highest, wherein the neighboring voxels are in awindow sized as a fraction of a number of voxels along each dimension ofa common registration grid.
 18. The machine-readable medium of claim 17,further comprising determining the displacement of the peak bycalculating a centroid of the voxel intensities of the neighboringvoxels inside the window.
 19. The machine-readable medium of claim 11,wherein the first medical image and the second medical image areobtained using different imaging modalities.
 20. The machine-readablemedium of claim 11, the correcting comprising causing translating apatient by causing movement of a patient couch or bed.